A164346 -id:A164346 - cp's OEIS frontend

A375776 Bitwise conflict-free sequence: Each number n is placed into the first set k that contains no element x where n AND x > 0: a(n) = k.

1, 1, 2, 1, 3, 4, 5, 1, 4, 3, 6, 2, 7, 8, 9, 1, 8, 7, 10, 6, 11, 12, 13, 5, 14, 15, 16, 17, 18, 19, 20, 1, 12, 11, 17, 10, 15, 14, 21, 13, 22, 23, 24, 25, 26, 27, 28, 2, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 1, 19, 18, 25, 16, 23, 22, 36, 10, 30, 29, 32

Offset: 1

Matt Donahoe, Aug 27 2024

			For n = 1, a(1) = 1 because 1 gets put into the first set.
For n = 2, a(2) = 1 because 2 AND 1 == 0, so 2 can also be put into the first set.
For n = 3, a(3) = 2 because 3 AND 1 == 1, so 3 must be put into a new set.

Alois P. Heinz, Table of n, a(n) for n = 1..16384
Wikipedia, Bitwise operation

Cf. A000079, A164346, A279125.

s:= proc() {} end:
a:= proc(n) option remember; local k; for k
      while ormap(x-> Bits[And](x, n)>0, s(k)) do od;
      s(k):= {s(k)[], n}; k
    end:
seq(a(n), n=1..75);  # Alois P. Heinz, Aug 27 2024

seq(n)={my(a=vector(n), L=vector(n)); for(n=1, n, for(j=1, oo, if(!bitand(n,L[j]), L[j]=bitor(L[j],n); a[n]=j; break))); a} \\ Andrew Howroyd, Aug 27 2024

def seq(n):
    L = [0] + [0] * n
    for i in range(1, n + 1):
        k = next((k for k in range(1, len(L)) if i & L[k] == 0), None)
        L[k] |= i
        yield k

a(n) = 1 <=> n in { A000079 }. - Andrew Howroyd, Aug 27 2024
a(n) = 2 <=> n in { A164346 }. - Alois P. Heinz, Aug 27 2024
a(n) = A279125(n) + 1. - Rémy Sigrist, Aug 30 2024

A166976 Array of A002450 in the top row and higher-order differences in subsequent rows, read by antidiagonals.

Original entry on oeis.org

0, 1, 1, 3, 4, 5, 9, 12, 16, 21, 27, 36, 48, 64, 85, 81, 108, 144, 192, 256, 341, 243, 324, 432, 576, 768, 1024, 1365, 729, 972, 1296, 1728, 2304, 3072, 4096, 5461, 2187, 2916, 3888, 5184, 6912, 9216, 12288, 16384, 21845, 6561

Offset: 0

Paul Curtz, Oct 26 2009

			The array starts:
0,   1,   5,  21,  85, 341,1365,5461,21845,87381,349525,    A002450
1,   4,  16,  64, 256,1024,4096,16384,65536,262144,1048576, A000302
3,  12,  48, 192, 768,3072,12288,49152,196608,786432,       A002001, A164346, A110594
9,  36, 144, 576,2304,9216,36864,147456                     A002063, A055841

A002450 := proc(n) (4^n-1)/3 ; end proc:
A166976 := proc(n,k) option remember; if n = 0 then A002450(k) else procname(n-1,k+1)-procname(n-1,k) ; end if; end proc: # R. J. Mathar, Jul 02 2011

T(0,k) = A002450(k). T(n,k) = T(n-1,k+1) - T(n-1,k), n > 0.

A174971 Periodic sequence: Repeat 3, -3.

Original entry on oeis.org

3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3

Offset: 0

Klaus Brockhaus, Apr 04 2010

Interleaving of A010701 and -A010701; signed version of A010701.
Essentially first differences of A010674.
Inverse binomial transform of 3 followed by A000004.
Second inverse binomial transform of A010701.
Third inverse binomial transform of A007283.
Fourth inverse binomial transform of A000244 without initial term 1.
Fifth inverse binomial transform of A164346.
Sixth inverse binomial transform of A005053 without initial term 1.
Seventh inverse binomial transform of A169604.
Eighth inverse binomial transform of A169634.
Ninth inverse binomial transform of A103333 without initial term 1.
Tenth inverse binomial transform of A013708.
Eleventh inverse binomial transform of A093138 without initial term 1.

Index entries for linear recurrences with constant coefficients, signature (-1).

Cf. A010701 (all 3's sequence), A000004 (all zeros sequence), A007283 (3*2^n), A000244 (powers of 3), A164346 (3*4^n), A005053 (expand (1-2x)/(1-5x)), A169604 (3*6^n), A169634 (3*7^n), A103333 (expand (1-5x)/(1-8x)), A013708 (3^(2n+1)), A093138 (expand (1-7x)/(1-10x)).

&cat[ [3, -3]: n in [0..41] ];
[ 3*(-1)^n: n in [0..83] ];

PadRight[{},120,{3,-3}] (* or *) NestList[-1#&,3,120] (* Harvey P. Dale, Dec 30 2023 *)

a(n)=3*(-1)^n \\ Charles R Greathouse IV, Jun 13 2013

a(n) = 3*(-1)^n.
a(n) = -a(n-1) for n > 0; a(0) = 3.
a(n) = a(n-2) for n > 1; a(0) = 3, a(1) = -3.
G.f.: 3/(1+x).

cp's OEIS Frontend

A375776 Bitwise conflict-free sequence: Each number n is placed into the first set k that contains no element x where n AND x > 0: a(n) = k.

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A166976 Array of A002450 in the top row and higher-order differences in subsequent rows, read by antidiagonals.

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Maple

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A174971 Periodic sequence: Repeat 3, -3.

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Magma

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